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How to Find the Greatest Common Factor (GCF)

ByMinul Hasan Chowdhury
Math

In this blog, we explore what the Greatest Common Factor (GCF) is, why it’s useful in everyday math, and how to find it using three different methods: listing factors, prime factorization, and the Euclidean algorithm. We also introduce MathTechLab’s free, easy-to-use GCF Calculator — a tool that quickly finds the GCF of any set of numbers while showing step-by-step solutions.

When working with numbers — whether you’re simplifying fractions, factoring expressions, or solving problems in everyday life — one concept you’ll come across often is the Greatest Common Factor (GCF).

In this post, we’ll break down what the GCF is, how to find it step by step, and introduce a handy tool from MathTechLab to make your calculations faster and easier.

📚 What is the Greatest Common Factor (GCF)?

The Greatest Common Factor (GCF) — also known as the Greatest Common Divisor (GCD) — is the largest number that divides two or more numbers without leaving a remainder.

  • The GCF of 12 and 18 is 6
  • The GCF of 24 and 36 is 12

Finding the GCF is useful for:

  • Simplifying fractions
  • Factoring numbers and expressions
  • Solving ratio problems
  • Working with multiples and divisibility

✏️ How to Find the GCF

Let’s look at a few common methods for finding the GCF:

Method 1: List of Factors

  1. List all the factors of each number.
  2. Identify the largest number that appears in both lists.

Example: Find the GCF of 18 and 24.

  • Factors of 18: 1, 2, 3, 6, 9, 18
  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Common factors: 1, 2, 3, 6
GCF: 6

Method 2: Prime Factorization

  1. Break each number into its prime factors.
  2. Multiply the common prime factors.

Example: Find the GCF of 30 and 45.

  • Prime factors of 30: 2 × 3 × 5
  • Prime factors of 45: 3 × 3 × 5

Common prime factors: 3 × 5 = 15
GCF: 15

Method 3: Division Method (Euclidean Algorithm)

  1. Divide the larger number by the smaller number.
  2. Take the remainder.
  3. Replace the larger number with the smaller one and the smaller with the remainder.
  4. Repeat until the remainder is zero.
  5. The last non-zero remainder is the GCF.

Example: Find the GCF of 48 and 18.

  • 48 ÷ 18 = 2 (remainder 12)
  • 18 ÷ 12 = 1 (remainder 6)
  • 12 ÷ 6 = 2 (remainder 0)

GCF: 6

📲 Find the GCF Instantly with MathTechLab’s Free Calculator

Doing these steps by hand is great for practice, but when you’re short on time or working with big numbers, our GCF Calculator can do the work for you in seconds.

  • ✅ Supports any two or more numbers
  • ✅ Shows the step-by-step process (factors and prime factorization)
  • ✅ Clean, ad-free, and fast
👉 Try the GCF Calculator

🎯 Final Thoughts

Whether you’re a student, teacher, or math enthusiast, knowing how to find the Greatest Common Factor is a useful skill that makes other topics — like simplifying fractions and working with ratios — much easier.

And when you need a quick solution, MathTechLab’s free GCF Calculator is ready to help. Bookmark it, share it with friends, and simplify math problems faster!

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